"What is the order of the ossicles in the inner ear that transmit the sound from the tympanic membrane to the scala vestibule?"

Malleus, Incus and stapes.

Explanation:

The three ear ossicles , located in the middle ear named as  Malleus(hammer) , incus (anvil) and stapes (stirrup).

The small cavity surrounding the bones of the middle  ear is called  tympanic cavity.

Auditory ossicles form a system of  levers which are linked together and are driven by the eardrum.The movement of the eardrum sets the hammer anvil and stirrup simultaneously. Finally results in creation of compression waves in the fluid of inner ear.  

And this is how the sound wave travels in the ear.